For each binary with identified encounter candidates, we present the distributions of their distance to Galactic spiral arm projected onto the Galactic Plane (X and Y galactocentric coordinates), since the spiral arms are assumed to be strictly located at Z=0. Encounter candidates were selected by using the 2D time-distance histograms that are produced by the bootstrap procedure. They were convolved with the histogram of the typical width of a galactic spiral arm, that depends on the galactocentric radius of the point considered, which is time-dependent. We used the value of 42 pc kpc\(^{-1}\)  provided in [1]} for the typical width of all spiral arms. After marginalizing the convolution over the distance, we obtained a probability distribution of binary-spiral arm encounter with time.
